I am very confused and I want to know what it means, but also if it means like 'broken swords', how and where can I fix them?
It indeed means both your swords are damaged.
For reference, here is a cropped screenshot of a moment during gameplay where the silver sword (left sword icon, with the typical angled cross guard) and all armour except for the gauntlets are damaged:
Using weapons and gear will slowly decrease their condition (hitting objects and receiving hits, respectively), and lower their stats, as indicated in red negative values on the item's description in your inventory. You can keep using the items in this state, but their ineffectiveness will keep increasing.
The icons on your HUD show up as red when the condition of the item drops to or below 50%.
As for repairing these items, there's an existing Q&A here on Arqade which handles that aspect.