1. why do we need to preach the gospel?

Matthew 28: 耶稣进前来，对他们说：“……你们要去，使万民作我的门徒，奉父、子、圣灵的名给他们施洗……”
Mark 16: 他又对他们说：“你们往普天下去，传福音给万民听……”
John 20: 耶稣又对他们说：“愿你们平安！父怎样差遣了我，我也照样差遣你们。”

as such, gospel is an obligation, given to us by the direct command of JESUS our LORD. it's easy to see why HE wanted us to spread his gospel.

John 3: 约翰说：“……父爱子，已将万有交在他手里。信子的人有永生；不信子的人得不著永生（原文作“不得见永生 ”），　神的震怒常在他身上。”
John 14: 耶稣说：“我就是道路、真理、生命；若不藉著我，没有人能到父那里去。”

2. what does it mean by preaching the gospel?

to finish quoting the passages above,

Matthew 28: “……所以，你们要去，使万民作我的门徒，奉父、子、圣灵的名给他们施洗。凡我所吩咐你们的，都教训他们遵守，我就常与你们同在，直到世界的末了。”
Mark 16: “你们往普天下去，传福音给万民（“万民”原文作“凡受造的”）听。信而受洗的，必然得救；不信的，必被定罪。……”

and again,

Luke 24: “照经上所写的，基督必受害，第三日从死里复活，并且人要奉他的名传悔改、赦罪的道，从耶路撒冷起直传到万邦。你们就是这些事的见证。……”
Acts 1: “父凭著自己的权柄所定的时候、日期，不是你们可以知道的。但圣灵降临在你们身上，你们就必得著能力；并要在耶路撒冷、犹太全地和撒马利亚，直到地极，作我的见证。”

I won't bother explaining what the gospel is. if you already are a believer, then you know what it is. caleb also expanded on the details quite a bit.

the only key to preaching the gospel is "preach". the only key to spreading the good news is "spread". it doesn't matter how you do it.

3. why do I preach or not preach the gospel?

obviously, there are other, more personal factors involved, whether a person decides to preach the gospel at a certain time, or in a certain place.

take me, for example, I often preach the gospel for one of several reasons:
1. because it's the command of JESUS, and because I am a christian;
2. because JESUS loves us and gave up His life for all of us, not just me;
3. because I love/like a person, and want to share with him/her the divine gift;
4. because I am explaining my faith to someone who is interested in my faith;
5. because I am defending my faith from non-believers or from false teaching;
...

and it usu. does not take place for one of several reasons:
1. the place/time is not appropriate for gospel;
2. I am afraid of the ridicule I might face;
3. I am too caught up in my own problems;
4. I feel lazy;
...

as you can see, apart from the first point, there really is no one good excuse why I don't preach the gospel whenever and wherever possible. the only reason why I don't do it is because of my very own imperfections and deficiencies.

hope it helps.