We can easily do it by using sections in table view. Add a button or tap gesture to section header and handle the action by using following code:

To open:

    [self.tableView beginUpdates];
    [self.tableView insertRowsAtIndexPaths:indexPathsToInsert withRowAnimation:UITableViewRowAnimationFade];
    [self.tableView endUpdates];

To close:

    [self.tableView beginUpdates];
    [self.tableView deleteRowsAtIndexPaths:indexPathsToDelete withRowAnimation:UITableViewRowAnimationFade];
    [self.tableView endUpdates];

where 'indexPathsToInsert' and 'indexPathsToDelete' are arrays of NSIndexPath objects.

   NSMutableArray *indexPathsToInsert = @[[NSIndexPath indexPathForRow:0 inSection:0]];
   NSMutableArray *indexPathsToDelete = @[[NSIndexPath indexPathForRow:0 inSection:0]];

Also we need to return "numberOfRowsInSection" to zero when we close the section and to required number of rows when we open it.

Following is a small example with single row being shown and hidden.

@interface DemoViewController () <UITableViewDelegate,UITableViewDataSource>
{
    BOOL isOpenFlag;
}

@property (nonatomic, weak) IBOutlet UITableView *tableView;

@end

@implementation DemoViewController

- (NSInteger)tableView:(UITableView *)tableView numberOfRowsInSection:(NSInteger)section {
    if (section == 0) {
        return isOpenFlag?1:0;
    } else {
        return 2;
    }
}

- (NSInteger)numberOfSectionsInTableView:(UITableView *)tableView {
    return 2;
}

- (void)closeSection {
    NSArray *indexPathsToDelete = @[[NSIndexPath indexPathForRow:0 inSection:0]];
    [self.tableView beginUpdates];
    [self.tableView deleteRowsAtIndexPaths:indexPathsToDelete withRowAnimation:UITableViewRowAnimationFade];
    [self.tableView endUpdates];
}

- (void)openSection {
    NSArray *indexPathsToInsert = @[[NSIndexPath indexPathForRow:0 inSection:0]];
    [self.tableView beginUpdates];
    [self.tableView insertRowsAtIndexPaths:indexPathsToInsert withRowAnimation:UITableViewRowAnimationFade];
    [self.tableView endUpdates];
}

- (UITableViewCell*)tableView:(UITableView *)tableView cellForRowAtIndexPath:(NSIndexPath *)indexPath {
    UITableViewCell *cell = [tableView dequeueReusableCellWithIdentifier:@"cell" forIndexPath:indexPath];
    [cell.textLabel setText:[NSString stringWithFormat:@"Cell %d",indexPath.row]];
    return cell;
}

- (UIView*)tableView:(UITableView *)tableView viewForHeaderInSection:(NSInteger)section {
    UITableViewCell *header = [tableView dequeueReusableCellWithIdentifier:@"cell"];

    if (section==0) {
        [header addGestureRecognizer:[[UITapGestureRecognizer alloc] initWithTarget:self action:@selector(tapSection)]];
        header.textLabel.text = @"Tap to open";
    } else {
        header.textLabel.text = @"NextSection";
    }

    UIView *view = [[UIView alloc] initWithFrame:[header frame]];
    header.autoresizingMask = UIViewAutoresizingFlexibleHeight | UIViewAutoresizingFlexibleWidth;
    [view addSubview:header];

    return view;
}

- (void)tapSection {
    isOpenFlag = !isOpenFlag;
    if (!isOpenFlag) {
        [self closeSection];
    } else {
        [self openSection];
    }
}

https://github.com/jeantimex/ios-swift-collapsible-table-section have a look at this