In all judgements in which a relation between subject and predicate is thought, this relation is possible in two ways. Either the predicate B belongs to the subject A as something which is (covertly) contained in the concept A; or B lies outside concept A, though connected with it. In the former case I call the judgement analytic, in the latter synthetic. Kant, Critique of Pure Reason, p.43

In synthetic judgements the connection of the predicate with the subject is thought without identity. […] Those add to the concept of the subject a predicate that had not been thought in it at all, and that could not have been extracted from it by any analysis. […] Empirical judgements, as such, are all synthetic. In synthetic judgements […] I add […] the predicate synthetically to the concept. For although neither of the concepts [the subject and the property/relation attributed as predicate] is contained in each other, yet they belong to each other, though only contingently, as parts of a whole, namely, of an experience which is itself a synthetic combination of intuition Kant, Critique of Pure Reason, p.43-44

Analytic judgements are therefore those in which the connection of the predicate with the subject is thought through identity. […] they are called elucidatory because […] nothing is added through the predicate to the concept of the subject, and the concept is only analyzed and broken up into its constituent concepts which had all along been thought in it (though confusedly). […] Kant, Critique of Pure Reason, p.43

In synthetic a priori judgements, this help [of experience] is entirely lacking. If I am to go beyond the concept A, and to know that another concept B is connected with it, then what is that on which I rely and which makes the synthesis possible, considering that I cannot have the advantage of looking about in the field of experience? Take the proposition: Everything that happens has its cause. The concept of a cause is entirely outside that concept [the event that happened] and indicates something different from that which happens; hence it is in no way contained in that representation. How then can I predicate of that which happens something totally different from it […] as belonging to it, and belonging to it necessarily? What is here the unknown […] on which the understanding relies when it believes it discovers, outside the concept A, a predicate B foreign to concept A, which it nevertheless believes to be connected with that concept? It cannot be experience, because the above principle, that all which happens has its cause, has added this second representation to the first, not only with greater generality, but also with the character of necessity, and therefore entirely a priori and from mere concepts. Upon such synthetic, i.e., expansive, principles rests the whole final aim of our speculative a priori knowledge; for the analytic principles are no doubt very important and necessary, but only to arrive at that distinctiveness of concepts which is requisite for a safe and wide synthesis as will lead to a genuinely new acquisition of knowledge. Kant, Critique of Pure Reason, p.44-45

Examples of analytic judgements: - All bachelors are unmarried - All triangles have three sides https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction