PS, as a fair warning, this may get kind of messy, though I will try to keep it from delving too far into messy. I will be using the phrase man/woman and his/her, even though I know there are many more genders and sexes out there.
Consent - (n) permission for something to happen or agreement to do something. (v) give permission for something to happen.
It cannot be given under durress. Situation - Man/woman pressures man/woman into having sex with them. Man/woman finally relents. This is not consent.
It cannot be given while drunk and/or high. Situation - Sober man/woman makes out, and eventually has sex with, drunk man/woman. This is not consent.
It has an age limit (in most states/countries) in place to protect those who are not old enough to form mature emotional relationships. Situation - An infant/three year old is taken advantage of by a close family member, teacher, pastor. Sixteen year old is coerced into sex by his/her boyfriend/girlfriend or teacher. A more-famous-than-usual person forms a sexual relationship with a minor. This is not consent.
It can be retracted. Situation - Man/woman says that he/she wants to have sex, gets weirded out/really just doesn't want to anymore and changes his/her mind, but the ther man/woman forces them to. Man/woman is in the middle of a blow job, and other man/woman jokingly says that he/she will shove it deep into their throat and, ignoring their partner completely when they say NOT TO DO THAT, does so anyway. This is not consent.
It can apply to touch as well. Situation - Man/woman touches man/woman's ass without asking. This is not a situation where consent was given.
All of the above situations are rape and molestation. They are wrong, and they do irreperable damage to the victims.
Consent is something that occurs between two, sober, adults over the age limit (17 in Texas) who agree to partake in sexual things with each other. This includes all things sexual - oral, vaginal, anal, standard, BDSM (which needs an entirely different level of communication), and anything else under the sun that you can think of. It is verbal; do not rely on non-verbal cues. A YES must be given; a 'no' or 'I guess' or 'fuck, fine' or 'okay' are not good enough. If in doubt of whether or not someone wants to be touched, or be sexually active with you, ASK; clear, concise, verbal communication is key.
Most importantly, minds change. It takes a true scumbag to cause someone who is uncomfortable in a situation, and is saying no, to feel bad. Accept it and move forward. Don't be that scumbag.