the marginal distribution
Given the joint picture of two variables, you sometimes care about just one of them and want to ignore the other. The marginal distribution of X is simply the distribution of X on its own, recovered from the joint by averaging away the variable you are not interested in.
The recipe is to sum (discrete) or integrate (continuous) over all values of the other variable. For a joint pmf p(x, y), the marginal pmf of X is p_X(x) = sum over all y of p(x, y) — add up each row of the table. For a joint pdf f(x, y), the marginal pdf is f_X(x) = integral over all y of f(x, y) dy — collapse the surface onto the x-axis. The name comes from the old habit of writing those row and column totals in the margins of the probability table.
Marginalising throws information away: it tells you about X but says nothing about how X and Y relate. That is why you cannot rebuild the joint from the two marginals — the two margins are consistent with independence, with strong dependence, and with everything between. Going the easy direction (joint to marginal) always works; going back does not.
From the joint table of (first die, sum of two dice), summing each row over all sums recovers the marginal of the first die: each face 1 through 6 with probability 1/6. The detailed link between the first die and the sum is lost in that summing.
A marginal is the joint summed (or integrated) over the other variable — and dependence info is lost.
Two marginals never determine the joint. Identical margins can hide wildly different dependence — that is why the joint, not the margins, is the complete description.