When you first create a chart in Excel, normally there is no Axis title in the chart. Please see the steps below to add the Axis titles:
Step 1: If you work with Excel 2016 or after, you can use the element handle. Click on the chart and you will see 3 icons appear on the right of the chart;
Step 2: Click on the plus sign, you will see the list of the "Chart Elements" such as Axis, Axis Titles, Chart Title, etc;
Step 3: Check the box in front of the "Axis Titles", you will see the Axis title appear both at the bottom for X-Axis, and on the left for Y-Axis;
Step 4: If you only want to keep the X-Axis title or the Y-Axis title, you either delete one if you get both or click the triangle after "Axis Titles" and select "Primary Horizontal" or "Primary Vertical".
If you work with an earlier version (or any version), you can get the chart title back with the steps below:
Step 1: Click on the chart and you will see the "Design" tab from the ribbon;
Step 2. In the "Design" Tab, click "Add Chart Element";
Step 3. Click "Axis Titles" and select "Primary Horizontal" or "Primary Vertical";
Step 4. You will see the Axis title now appear in the chart.