Error Implementing free dictionary Api in discord.py

Your error does not come from the API call to the dictionary api, but rather from your call to the discord api.
The error message says discord.errors.HTTPException: [...] In embed.fields.2.value: This field is required.
So the error comes from an empty field in your embed! The field has index 2 so it is actually the third field (Synonyms) which is causing the problem.
You can simply check if a string is empty, before even adding the field. And if it is empty, just don't add it.

deffinal= discord.Embed(title=f"`{word.upper()}`")
if meaning:
    deffinal.add_field(name = "Definition", value=f"{meaning}")

if example:
    deffinal.add_field(name = 'Example', value = f"{example}")

if synonyms:
    deffinal.add_field(name = "Synonyms", value = f"{synonyms}")

@client.command()
async def mean(ctx,word):  
    response = requests.get(f"https://api.dictionaryapi.dev/api/v2/entries/en/{word}")
    if response.status_code == 404:
        await ctx.send("No such word")
        return
    else:
        wordx = response.json()
        the_dictionary = wordx[0]
        meanings = the_dictionary['meanings']
        definitions = meanings[0]
        definition = definitions['definitions']
        meaningg = definition[0]
        meaning = meaningg['definition']
        example = meaningg.get('example',['None'])
        synonymslist = meaningg.get("synonyms",['None'])
        if isinstance(synonymslist,str):
            synonymslist = [synonymslist]
            pass
        synonyms = ','.join(synonymslist)

        deffinal= discord.Embed(title=f"`{word.upper()}`")
        if meaning:
            deffinal.add_field(name = "Definition", value=f"{meaning}")

        if example:
            deffinal.add_field(name = 'Example', value = f"{example}")

        if synonyms:
            deffinal.add_field(name = "Synonyms", value = f"{synonyms}")

        await ctx.channel.send(embed = deffinal)

Adding to itzFlubby answer, using requests will be blocking read more which means if you block for too long then your bot will freeze since it has not stopped the function’s execution at that point to do other things.

Here is the final code, also I changed the format a bit to make it easier to read.

# import aiohttp

@bot.command()
async def mean(ctx, word):
    async with aiohttp.ClientSession() as session:
        async with session.get(f"https://api.dictionaryapi.dev/api/v2/entries/en/{word}") as r:
            if r.status == 200:
                info = await r.json()
            else:
                return await ctx.reply("No such word")

    the_dictionary = info[0]['meanings'][0]['definitions'][0]

    definition = the_dictionary.get('definition')
    example = the_dictionary.get('example')
    synonymslist = the_dictionary.get("synonyms")

    # if only one synonym is avaliable
    if isinstance(synonymslist, str):
        synonymslist = [synonymslist]
    synonyms = '\n'.join(synonymslist)

    deffinal = discord.Embed(title=f"`{word.upper()}`")
    if definition:
        deffinal.add_field(name="Definition", value=f"```{definition}```")

    if example:
        deffinal.add_field(name='Example', value=f"```{example}```")

    if synonyms:
        deffinal.add_field(name="Synonyms", value=f"```{synonyms}```")

    await ctx.reply(embed=deffinal)