Something that's unswerving follows a direct path. Because an unswerving person or thing never turns aside, the word is also commonly used to describe steadfast loyalty, like a dog's unswerving devotion to its master.
The adjective unswerving often describes loyalty. Your best friend's unswerving loyalty to you, for example, feels secure and dependable — you know she'll always be there for you. You can also use the word more literally, when you talk about something moving in a straight, unswerving line, never making a turn or detour. The verb swerve is at the root of unswerving — originally, it meant "to depart," but by the fourteenth century its meaning was "to deviate from a straight course."