A lot of the definitions that Christians have of it are in reaction to extremes within the Pentecostal movement. So, a lot of people will say that it's about love rather than about the simple baptism with power that it really is. A lot of people will say that it's the power to have godly character and while perhaps if you mix the power with faith you can experience some of those changes in your character, far too many people have horror stories about Pentecostal Christians, healing evangelists, etc. where they were real characters alright!
Ideally, it's the power to share the Gospel with others in a supernatural demension where signs and wonders are following your testimony. That grows out of the speaking in other tongues. The speaking in other tongues is the door to the other manifestations of the Holy Spirit. The more that I personally pray in other tongues, then in direct proportion I have greater manifestations of discerning of spirits, word of wisdom, word of knowledge, interpretation of tongues, gifts of healings, workings of miracles, other types of prophetic utterances, visions, dreams, and diverse kinds of tongues. The private devotional form of tongues sorta gives birth to those times when you'll ""accidentally"" blurt out something in other tongues that'll be understood by someone understanding that language or in a form where there's tongues and interpretation of tongues, etc.
The biggest part of the importance of the baptism with the Holy Spirit is both the relief you can bring to others with the times of refreshing that you're able to bring them from the Presence of the Lord, and that being lead by the Lord is sooo much easier. The Scriptures become MORE PRECIOUS when you're really filled with the Holy Spirit 'cause it's practically the Author Himself reading them through your eyes.
It's the opening up of the spiritual realm to you, so sometimes the attacks on the negative side of the spectrum are much more intense 'cause you're more dangerous to the devil when you can bypass your intellect and what your brain knows and speak directly from your spirit to God about all that's going on in your life and in the life of others that you know WITHOUT INACCURACY. If I start praying in other tongues for you right now, it'll be all up in all of your business, detail by detail, whether or not our heavenly Father ever allows me to have the interpretation for my mind and for anything applicable to share with you. It's praying the perfect will of God at all times and giving thanks well when you're functioning in what some would call the private devotional form of speaking in other tongues. There's nothing like it. It's worth pursuing. It brings a new demension of the Presence of God into your life.
It basically winds up taking the same heat from other Christians as UR, so on the persecution level you're probably already used to some of that
None of the ministers that are on television today that really take a whole lot of heat, even from some UR folks, function without the baptism with the Holy Spirit. If there were no baptism, then there'd be no talk of the supernatural in their meetings and the persecution's over with about the anecdotal evidence that some will bring against the Holy Spirit that someone got prayed for and died anyway. Where there are no greater expectations, then where's the beef? Someone got prayed for and died. Big deal, right? So, some of the heat that many of them are taking winds up being a form of validation 'cause they wind up taking more heat than the local pastor would have who wasn't baptized with the Holy Spirit and simply gave "last rites/rights" or whatever.
It's the ability to wage a good warfare, in St. Paul's way of describing it. 1Corinthians 14 says that you give thanks well, but the other person isn't edified if you don't say something in their language. It's just an extra-demension of the Holy Spirit that most Christians long for anyway, but many don't realize that this is what it's going to look like if they really wanna go there. All Christians have the Holy Spirit, but the Holy Spirit doesn't have all Christians, if that makes any sense. Not sure how to say that in a clearer way.
It's a deeper demension of yeilding to the Holy Spirit day by day. That's probably the best way that I can describe it. People get fixated on power, the results that'll accompany it as you're taking the Gospel to others in a context where it's going to be believed, etc. But the Spirit-filled life is really the life of continual surrender on the deepest levels possible for a human being to the Holy Spirit. You become more aware of the Holy Spirit as a Person. He's more real to me than you'd be if you were in the same room with me. If I hugged you, the Holy Spirit would still be more real to me. It takes your worship time into a whole other, deeper level.
Some books get into all of the debates as to whether it's actual power or enabling when it's really both. Sharing the Word becomes easier 'cause so often there will be more flashes of it not being you that's speaking, but Him. It's essentially a whole new door that opens to you, but you still have to decide to take each step daily expecting Him to be there and to lead and train you into how to make the greatest impact possible on people for Jesus Christ.
Again, some of the mental and emotional and other types of persecution can intensify sometimes and as with all persecution, it's just for seasons, but you wind up taking much closer, much deeper looks into the 2Corinthians 3 mirror. I said earlier that it wasn't about character or love, although none of the power works without love and solid character, but at the same time I sincerely believe that in talking about the 2Corinthians 3 "being transformed from glory to glory" that there does come a point in every single believer's life where they will not be able to get the rest of the way without the baptism with the Holy Spirit. Ultimately the baptism does become a vision issue 'cause the baptism is a bigger mirror, using the 2Corinthians 3 analogy:
17 Now the Lord is that spirit, and where the Spirit of the Lord is, there is libertie. 18 But we all, with open face beholding as in a glasse the glory of the Lord, are changed into the same image, from glorie to glorie, euen as by the spirit of the Lord. (2Cor 3:17-18 KJV 1611)
The book of Acts draws attention to boldness being a part of being filled with the Holy Spirit. It says a time or two that when they were filled again with the Holy Spirit (I'm thinking Acts 4) that they spoke the Word of God with boldness afterwards.