A peptide is a short chain of amino acids, linked end to end by a peptide bond, the same bond that holds proteins together. The only real difference between a "peptide" and a "protein" is length and convention: short chains (roughly 2 to 50 amino acids) are usually called peptides, longer folded chains are called proteins, and the line between them is a matter of usage more than a hard rule.
The amino acid sequence is what gives a peptide its identity and its shape, and its shape is what determines what it can bind to or signal to in the body. Because they're small and specific, naturally occurring peptides already do a lot of work in human biology (insulin is a peptide hormone, for instance), which is part of why synthetic peptides attract research interest: the body already has machinery built to recognize peptide-shaped signals.
That specificity is also why peptide research is unusually dependent on verification. A peptide that's the wrong sequence, degraded, or contaminated won't just underperform. It can behave completely differently, or not bind at all. That's the whole reason certificates of analysis exist in this space: identity (is this the sequence it claims to be) and purity (how much of the sample is that sequence versus something else) are not optional details, they're the two questions a peptide sample has to answer before anything else about it matters.
Peptides are typically supplied freeze-dried (lyophilized) rather than in solution, because a dry powder is far more stable in storage and shipping than a reconstituted liquid, which degrades faster once mixed.