What is counterparty risk?
As defined by Investopedia, counterparty risk is:
"The risk to each party of a contract that the counterparty will not live up to its contractual obligations."
In the world of cryptocurrency, counterparty risk does come into play in specific circumstances; while decentralized, open blockchains like BTC are designed specifically to eliminate counterparty risk, some assets do carry this risk as it is inherent to their design.
Digital assets that are tied to real-world commodities or Government-issued fiat currencies are good examples of assets that carry counterparty risk. These assets are dependent upon a company holding enough of a given currency or commodity to "back" the digital currency in circulation. The risk inherent to such a model is that the company issuing the digital asset may not actually own or control the real-world asset to back the digital counterpart.
This class of cryptocurrencies, known as stablecoins, are particularly susceptible to counterparty risk as stablecoins achieve relative "price stability" by holding as collateral the underlying asset in question. Stablecoins that are backed by US Dollars illustrate this risk, as the company issuing the coin may not actually have the US Dollars on hand sufficient to back the digital asset.
Note: Counterparty risk is commonly discussed in the cryptocurrency sphere as it pertains to holding coins on a centralized exchange. Doing so introduces counterparty risk as the centralized exchange controls your private keys, and thus, may or may not have enough funds on hand to cover every depositor.
Exodus itself, however, is not a centralized exchange and does not store private keys or sensitive user data in any form. The Exodus wallet itself is free of counterparty risk - however, certain assets within Exodus may carry this risk independent of the wallet software itself.