In a POSET, if an element a is related to some other element b (ie there is an upward path), we call these two elements comparable.
And if not; incomparable.
A chain is nothing but a sequence of distinct comparable elements.
An antichain is a sequence of distinct incomparable elements. Note than a lone element is an antichain despite being comparable to itself.
If the length of the longest chain is n, there are are least n antichains.
Source: https://www.researchgate.net/figure/Two-possible-antichain-partitions-on-the-Hasse-diagram_fig3_313376303
Here, the longest chain is: $o\leq a\leq d\leq f\leq g\leq I$. Length is 5.
Antichain partitions are 6.
If the longest chain in a partial order is of length n, then the partial order can be written as a partition of n antichains.