CSV to HTML Converter
CSVReader
Reading a CSV file can be a complex task.  While many CSV files are just comma-separated-values, if a value contains a comma, it would be surrounded by double quotes, and if the value contains double quotes, the double quotes themselves are doubled.
To handle these more that just a basic CSV files, you really should use a CSV library, such as OpenCSV (com.opencsv:opencsv:5.0) or Apache Commons CSV (org.apache.commons:commons-csv:1.7).
HTML
Valid HTML
Your code essentially just writes &lt;table&gt;...table data...&lt;/table&gt;.  This isn't proper HTML.  You're missing &lt;html&gt;...&lt;/html&gt; tags around the entire document, and &lt;body&gt;...&lt;/body&gt; around the content.  You should probably also have a &lt;head&gt;...&lt;/head&gt;, perhaps with a nice &lt;title&gt;...&lt;/title&gt;.
Escaping
If your CSV data contains any special characters, like &lt;, &gt;, and &amp;, you really must escape them in the generated HTML table.
Table Headings
It looks like the first line of your table contains headings, not data.  The first table row should probably be formatted with &lt;th&gt;...&lt;/th&gt; tags instead of &lt;td&gt;...&lt;/td&gt; tags.
Line by Line processing
You are reading the entire CSV file into memory, and only when it has been loaded in its entirety are you writing it back out as HTML.  This is very memory intensive, especially if the CSV file is huge!
Instead, you could:

open the CSV
open the HTML file
write the HTML prolog
for each line read from CSV file:

format and write line to HTML file


write HTML epilog

Untested, coding from the hip, without handling quoting in CSV or escaping any HTML entities in output:
        try (BufferedReader reader = new BufferedReader(new FileReader(csvFile));
             FileWriter writer = new FileWriter(outputFile)) {

            writer.write(&quot;&lt;html&gt;&lt;body&gt;&lt;table border&gt;\n&quot;);

            String currentLine;
            while ((currentLine = reader.readLine()) != null) {
                writer.write(&quot;&lt;tr&gt;&quot;);

                for(String field: currentLine.split(&quot;,&quot;))
                    writer.write(&quot;&lt;td&gt;&quot; + field + &quot;&lt;/td&gt;&quot;);

                writer.write(&quot;&lt;/tr&gt;\n&quot;);
            }

            writer.write(&quot;&lt;/table&gt;&lt;/body&gt;&lt;/html&gt;\n&quot;);

        } catch (IOException e) {
            e.printStackTrace();
        }

XML &amp; XSLT
You may want to consider creating a CSV to XML translator.
Your XML output might look like:
&lt;data input-file='ExampleInput.csv'&gt;
  &lt;person&gt;
    &lt;Name&gt;Ulbrecht&lt;/Name&gt;
    &lt;Vorname&gt;Klaus Dieter&lt;/Vorname&gt;
    &lt;Alter&gt;12&lt;/Alter&gt;
  &lt;/person&gt;
  &lt;person&gt;
    &lt;Name&gt;Meier&lt;/Name&gt;
    &lt;Vorname&gt;Bertha&lt;/Vorname&gt;
    &lt;Alter&gt;102&lt;/Alter&gt;
  &lt;/person&gt;
&lt;/data&gt;

And then you could use an XSLT Stylesheet to translate the XML to HTML, possibly in a browser without ever writing the HTML to a file.