EQ is essential for a tight mix. When you are transitioning between two songs and they are both playing out together, there would be a lot of issues without it. For beginners, this may be even more important than you realise, especially if you have never played on a loud sound system or are using sub-par speakers.
So I'm going to try and break it down as simply as possible. When two tracks are playing at once, there is a lot of frequencies that will clash. Kick drums and basslines are the worst for this, especially if they are in slightly different keys. But their low-frequency content takes up a lot of headroom and can be too much for some sound systems. On top of that too much will sound incredibly muddy. This brings us to the first rule of DJ EQ.
1. Never have two basslines running at once. If you have two tracks playing out in the mix, have one of the bass knobs up and one all the way down. It will be a lot cleaner if you just mix the mids and highs in with the current song. It will also stop the kicks clashing and knocking the people over if the subwoofers are punchy enough. When you want the track you are mixing into to take dominance, flip to the new bassline and turn the old track's bass all the way down. This is best done at the end of a musical phrase.
2. The Mid knob covers the vocal range, use that to your advantage. If you have a vocal that needs to be brought out and made more obvious, give the mid knob a small boost. This works well if you are using an acapella over an instrumental, give the mids of the acapella a boost and duck the mids of the instrumental track a wee bit to let the vocals sit nicely in. Conversely, if you are mixing two songs with vocals, as with basslines, they can often clash if they are playing at once. Removing all the mids won't remove the vocals on a track but it will allow the other tack to gain vocal dominance.
Other uses of mid can be to pronounce the bassline (some find this counter-intuitive, this works because a lot of the audible bits of bass instruments are in the lower mid range in the form of harmonics. This is a useful trick because it doesn't boost the sub frequencies which are headroom hungry.
3. The High knob is great for sexy hi-hats. In house music especially, the hi-hat off-beat is as important as the bassline. A small boost to the high knob may bring out the brilliance of a good hi-hat on a lesser system and, accent it on a good one. It will also be an essential knob to brighten up the mix and add clarity if a certain song, or the room itself is lacking in some. Likewise, if the song or room is too bright or people are getting sore ears, it may be a case of dropping the highs a bit.