Rule 801(d) contains two types of statement excluded from the definition of hearsay. Part (1) focuses on various kinds (but not all kinds) of prior statements by a witness. Since the witness is there on the stand, we can cross-examine him or her and get explanations of the statement, so there is no real reason to treat them as hearsay.
Prior inconsistent and prior consistent statements have to do with impeachment and rehabilitation of witnesses, which we will cover later.
Prior statements of identification refer to a common problem in criminal trials. When the defendant committed the crime while high on meth, he looked like a criminal. But now he's been out on bail for 18 months, and his lawyer has made him cut his hair, take a shower and wear nice clothes. When the trial finally takes place, most of the witnesses cannot ID him because his appearance has changed, so the police testify the witnesses picked him out of a lineup (cop testifies that a witness saw a lineup and said "That's him"). For an example of such an appearance change, see these before and after photos from the Portland, Oregon, sheriff's department.
The far more important category of excluded statements is part (2) -- admissions of the party opponent. Here, too, the opposing party is present in court and can explain, refute or place in context any prior statements they made, so there is no particular reason to treat them as hearsay.
The following problems will introduce you to the five kinds of admissions (note that "admissions" just means "statements" by the party -- the party does not have to "admit" anything).
1) Personal
2) Adopted
3) Authorized
4) By agents
5) Co-conspirator
These problems will also introduce you to two other hearsay concepts -- remainders and hearsay within hearsay.
