Meconium is the first manure a newborn foal produces. It's all the crap the foal swallowed while in the uterus, and it builds up in the colon - it's not expelled until birth. (All mammal infants produce meconium, including humans).
However, horses are more prone to difficulty passing the meconium (in humans, this is often the first sign of cystic fibrosis). Because horses are more prone to impaction in general, meconium impaction is pretty common, especially in colts. It's so common that some breeding farms just give a warm water enema to every single foal without waiting to see if they're having problems. The enema used is usually soapy water with a bit of mineral oil or lube. And, of course, giving a foal an enema is not exactly an easy task and has to be done very carefully.
The worst problem is that sometimes these foals lose their appetite, and end up dehydrated or don't drink the colostrum (essential for immune system health). Rarely, surgery is necessary.
Meconium is dark hard pellets, whilst a foal's "milk" manure is yellow and rather runny.