Not enough UTXO's will result in loss of privacy.

[successcouncil]

Is there anything I can do to avoid this?   And what does it actually mean?

[bitmover]

Is there anything I can do to avoid this?   And what does it actually mean?

This post is not related to only Armory Wallet, so I suggest moving this to Technical Discussion.

UTXO (Unspent transaction output) are bitcoins you received. Every transaction you received is a UTXO.
Those bitcoins can be tracked to who send them you.

For example, you have a verified account in coinbase and coinbase sent Bitcoins to your wallet. Someone can check your public address and see that your bitcoins came from coinbase, then they could ask coinbase who you are.
Then, when you sent those bitcoins to someone else, he can also discover who you are. This is how you lose your privacy with UTXO.

To avoid this, it is good to generate a new address for every transaction. It will improve your privacy, but it won't give you anonymity, because that "coinbase address" (which is linked to your ID) will not be your only one. People will never know for sure how many addresses you have, so nobody will know your total balance.

To have a pseudo anonymity (which is not 100%) you have to send those UTXO to a bitcoin Mixer, which will mix your UTXO and give you "clean" coins, which cannot be tracked back to you.

[goatpig]

Armory is warning that it has to unrelated UTXOs together to meet the value of your desired payment. This erodes your privacy because if you move forward with this transaction, all these UTXOs will now be related.

There is no risk of coin loss, just privacy loss. Financial privacy is significant however, don't damage if you don't need to.

What you can to go around the issue is manually select UTXOs you know are fine to mix/use for that particular payment.