QGIS
QGIS is the pre-eminent open source desktop GIS. It has functionality comparable to Esri's software, can be installed on a Mac, and it's free! You can find a long list of tutorials via this page.
OSGeo
QGIS is part of a broader suite of open source geospatial software project under the umbrella of OSGeo. Their website is a great place to explore all of the different tools available for use. Some of my favorites include PostGIS, GDAL/OGR, and GeoServer.