You might be referring to the USB Mass Storage Mode.
USB mass storage is the standard protocol used by flash drives,
external hard drives, SD cards, and other USB storage devices. It also
was used by Android devices and even many basic phones.
At some point most Android developers decided to discontinue with this handy feature. They have legitimate arguments or at least justifiable reasons against the feature. It was discontinued sometime since Android 4.3 and later versions don't have this feature.
As one reddit user explained the reasons behind such discontinuation:
Earlier Android used to have
/data partition for app data and
/sdcard for movies, music and rest. Say you are an app freak and
have installed lots of apps, what happens in /data fills up but still
you can't use space from your
/sdcard as it's a separate partition.
Now what Google has done is used unified file system. So that you can
share space between
/data. USB mounts storage on host
and gives entire block level access to the host. If this is done the
partition is unmounted from your phone. It was fine when /sdcard was
separate now since both
/sdcard reside on same partition
Android can't afford to allow full block access to another host. This
is solved with MTP.
Another reason, Microsoft holds patents for long file name support on
FAT filesystem. That's one patent for which they demand royalties
from OEM's. If you use USB mount, you need to format your
FAT because most users use windows. If you use
FAT, you need to pay
MS or risk a lawsuit. With MTP, Google can use
ext3/4 btrfs whatever
they please and there is no risk of lawsuit.
Finally, formatting filesystem with
ext3/4 instead of FAT gives lots of read/write improvements since Android uses linux kernel.
The new options, Media device (MTP) or Camera (PTP) mode, are either unavailable to earlier editions of Windows and particularly difficult to use on other OSes e.g. Linux , or too limited in terms of functionality as well UI feel.
USB Mass Storage on Android Devices