What are smart objects?

Does this have anything to do with changing a raster image to a vector image?

No.

Please post the image or a screenshot.

Photoshop Smart Objects can be embedded or linked files.

The advantages of Smart Objects are numerous:

• external files can be referenced and represented in layered documents

• multiple instances of a SO in a containing document that update simultaneously on saving an edited SO (please note that for a SO to maintain a connection to the external file one needs to use File > Place Linked instead of File > Place Embedded)

• the possibility of placing vector content as Vector Smart Objects (though this will output as pixels)

• non-destructive application of Filters

• non-destructive application of transformation, warp, puppet warp (not all of these are available for Vector SO, but by converting such a one to a regular SO they become applicable)

• combination of elements of different color spaces and bit depths

• the ability to Replace Contents of SO (for example when faking as-of-yet non-existent products by mapping packaging design elements onto images of a blank container and the design is likely to change)

• Stack Modes for certain combinations of photographic images

Smart Objects are layers that can save images losslessly when scaling down and up. Some effects are also non-destructive since their parameters are stored and can be changed later.

On the other hand you lose some features, mostly colour tools. For example Hue or Levels become unavailable.