For a trade to happen, there must be a buyer and a seller. The buyer could have placed an offer to buy, which the seller took. Or the seller could have placed an offer to sell, which the buyer took. These are the only two possibilities.
If the buyer placed the offer which the seller later took, the buyer is the maker (he made liquidity available) and the seller is the taker (they took the buyer's offer). If the seller placed the offer which the buyer later took, the seller is the maker (he made liquidity available) and the buyer is the taker (they took the seller's offer).
This matters for at least two reasons:
1) Typically the maker pays a lower fee than the taker.
2) This makes a difference in understanding what the price is telling you. For example, imagine if there's a market with people willing to sell apples for $1 and willing to buy apples for $0.90 -- if the price never changes, you will see transactions for $1 and transactions for $0.90, which might make you think the price is changing. But all the $1 trades will have the "buyer is not maker" flag and all the $0.90 trades will have the "buyer is maker" flag, allowing you to understand that the change in trade prices doesn't reflect any actual change in the market.