Those of us who have a difficult time remembering the meat fast should be grateful if you do not follow the Eastern rite…fasting from all animal products Wednesdays AND Fridays.

We have a calendar from our church, and it is helpful because it notes which days are fast days. (My husband always looks at the calendar when he gets down to the kitchen first thing in the morning!)
Meat, at least in early Christian times, was considered a feast food. It was not as readily available and usually people only had meat on special occasions. During Lent, we are awaiting that special occasion–the celebration of the Resurrection–and so we are fasting because Jesus is not with us! As he says, “Nobody fasts when the bridegroom is here.” Giving up meat is a small way of acknowledging the season of penance and waiting. For the same reason, the Eastern Churches have a “Nativity Fast”–a similar period of fasting and penance before Christmas.
It also helps us look forward to the Resurrection and the Nativity. One cannot truly appreciate a feast if one is sated before he sits at the table.
That said, I have certainly forgotten and had cheese or eggs on a Wed/Friday. I try to spend more time in prayer that day, or refrain from eating the rest of the day.
My priest gave an excellent sermon on fasting the other week. He pointed out that often it is hard, that we may grumble because we can’t have meat or eggs on a wednesday or friday during Lent—but to remember that to deny the fast is to deny Jesus. He did not deny us anything, he gave of his entire self to save us. His suffering was much greater than our inconvenience in not eating a particular food. This put it all in perspective for me, and I no longer see fasting as a trial, but a blessing.
ETA: as to why Wednesdays and Fridays; traditional Wednesday is the day that Jesus was betrayed by Judas, and Friday was the day He died on the cross.