There are several good file explorers available which offer network access. To have them accessing your Mac, you just need to setup shares. Here is a little howto which explains the Mac part1 for the first candidate I'll recommend you.
This is what I've used for years, and it's pretty convenient. Not only it allows you to browse your local files, it also allows to browse images (slideshow), videos, has an app manager, and more. In the context of your question, it supports a load of protocols to access the network and browse remote resources. I've successfully used it with SMB (it even auto-detects resources for this) and SFTP (see the howto I've already linked). To setup the connection, you simply open the app, goto Menu › Network › FTP …
Setup network connection with ES File Explorer (source: MJD; click images for larger variants)
… hit the + button, and fill in your data: "server" is the IP your Mac showed you (in the example1, it was
192.168.1.90), Port is fine with 22, Username/Password are your Mac credentials, Encoding you can leave on "auto", and in Display you can give it a name of your choice. Done: Now you should be able to browse your Mac files tapping the corresponding entry in the second screenshot above.
It will work similarly with other network-enabled file explorers. Two other candidates I could recommend you here are …
Completely open source and free, so no ads inside. Offers about the same features as ES File Explorer:
Open Explorer (source: Google Play; click images for larger variants)
You can see the networking section in the lower-left of the screenshots, where you can add more connections. I've used this one successfully with my Linux machine, so it definitely works.
I have not used this one myself, but saw it recommended quite frequently:
Solid Explorer (source: Google Play; click images for larger variants)
Here you see the networking capabilities in the second screenshot. Procede as described above.
All three apps are well rated in the stores. Which one to take depends on "personal preferences" (check a bit closer for additional features provided by each, as well as maybe requirements (they all work with Android 4.0+ at least), and maybe read some of their reviews (linked from my list). I'm pretty sure you'll find them all satisfying.
1: Basically: Open System Preferences › Select Sharing › In left hand pane check Remote Login › To the right you will now see something along the lines of To log in to this computer remotely, type "ssh [email protected]" (this is what you will need to setup the file explorer afterwards)