In an investment context, syndicates usually exist in order to spread risk.
Any financial institution (such as an investment bank) has a limited capacity to take risk. If it takes on too much risk, not only does it expose its shareholders to excessive risk, but because of the nature of its business, it also exposes its customers and counterparties to risk.
Large financial institutions may also create systemic risk by taking on too much risk. Because of this, and to protect depositors, regulators set limits on the exposure any one bank has to a single risk.
This means that risks that are too large for any one institution to take on by itself need to be spread out through syndication.
A simple example of syndication is when it occurs with bank loans. A major borrower may find it hard to raise a large loan from a single bank. If a group of banks form a syndicate the risk is spread over several banks. Usually, one bank will act as the lead manager of the the loan and handle most of the work involved.
Insurance may also be underwritten by a syndicate. This is common practice in the Lloyd's market.