There are 4 major divisions in the top tier of football in England.
The Premiership
The Championship
League 1
League 2
The three worst teams in the Premiership (Derby, Fulham and Bolton - if the season ended today) get relegated to the Championship and the three best teams in the Championship (Stoke, West Brom + play off winner) get promted to the Premiership. The teams finishing in 3rd, 4th, 5th & 6th play off for the third spot in the EPL and the three worst teams in the Championship get relegated to League 1 and so on.
As for the race for top 4 in the EPL this is because the top 4 teams qualify for the Champions League next year, a very lucrative and prestigious competition. The teams finishing in 5th, 6th and 7th will qualify for a lesser European competition called the UEFA Cup. With promotion/relegation and the fight for European places all at stake there are very few meaningless games at any time of the year, even now with only a handfull of games left.