My laptop currently has a maximum resolution of 1366×768, when not plugged into an external monitor, as shown here:
I have a monitor with 1080p display capabilities. Oddly, when I plug it in to my laptop, my laptop's screen immediately increases its maximum resolution:
However, everything seems to shrink and become more blurry. I don't believe my laptop supports 1080p resolution (it's a Lenovo Yoga 260, but not the FHD model). Furthermore, msinfo32 seems to report a maximum resolution of 1366×768 @ 60 hertz too. 
If someone could provide me some insight as to what's happening, that'd be great! It's not an issue, I can always readjust my resolution, but it's quite odd.
Clarification: I'm duplicating my screen to my external monitor.
Best Answer
It is because it is doing screen mirroring and assuming that the external display is your "primary" display. As a result it is rendering at the maximum "native" resolution and then scaling it down for your built in display.
The alternative would be setting it to your internal display resolution (1366x768) and scaling it up to the external display resolution of 1920x1080. This will result in the external display being blocky and looking bad
If you want two independent displays rather than one single mirrored display you will then have the option of using each display at its native resolution. I.e. 1366x768 for the internal display and 1920x1080 for the external.
You can cycle through the various options of internal and external displays by pressing Windows+P. The options you have are