Hana is right you can mostly see the fat on the outside of cuts of meat but some of it is 'marbled' , Its within the muscle. Unfortunately Its the fat that gives much of the flavour so very lean meat can have less flavour and can be dry.
Heres some info from a little diabetes cook book. To anyone else reading. Please don't shoot the messenger.
Where I've put low, moderate and high , the book says, choose for preference, eat moderately and avoid. With many of the cuts in the moderate section you can cook the meat with the fat and then cut off the visible fat. Its hard to do that with roast leg of pork with crackilig though!
I've just included the most usual cuts. but there are some regional variations in names so to confuse things, your butcher may use a different term.
Beef
low fat
mince at 5%, fillet, flan or skirt trimmed of surrounding fat.
Moderate
mince at 10%, sirloin, topside, silverside, rump steak, chuck or blade steak, neck
High
mince at 15-20%, ribs, shin, rib eye steak
Pork
low
fillet
moderate
leg, loin, gammon
high
shoulder, belly, ribs
Lamb
low
none
moderate
leg,
high
shoulder, saddle, neck, chump, scrag, breast
Veal
low
escalope, fillet (won't include the rest because they're not generally available)
Poultry and Game
low
wild duck(if you happen to find one!),
chicken and turkey without skin
all other game ie venison, hare rabbit
Moderate
duck,duck breast
Chicken and turkey with skin
guinea fowl,
chicken liver
high
goose
and foie gras!!!!
Offal
low
liver
(and if you're into them heart and tripe)
moderate
kidneys
(I'll miss out the rest cos I doubt many British people would eat them today)
Incidently, although there appears to be an awful lot of fat on duck it renders (melts) easily when cooking and probably is nearer in quality to the beneficial fats found in fish than that in other meats
As Hana says the way you cook it makes a big difference. You can, for example ,fry mince off in a pan, allowing the fat to melt and then drain it off. You can brown meat for a caserole, and then drain it on kitchen paper before putting in the liquid. After cooking a casserole or stew,allow it to cool down then you can skim off any surface fat. You can cook chops, steaks etc on a grill, griddle pan or portable electric griddle, once again allowing the fat to run off.