Gross
The raw score: 88 strokes is a gross 88. Simple, and fair only when everyone is roughly the same standard.
Net
Net subtracts your course handicap from your gross. A golfer who shoots 88 with a course handicap of 16 has a net 72.
Where the course handicap comes from
Under the World Handicap System it is: handicap index × (slope rating ÷ 113) + (course rating − par). A harder course (higher slope) gives you more strokes; an easier one fewer. That's why the same golfer gets a different number at different courses and tees.
Allowances
For some formats the published recommendation is to play off a percentage of the course handicap — for individual stroke play, 95%. Leagues can choose their own; the important part is choosing before the first round.